Arithmetic of singular Enriques surfaces
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We study the arithmetic of Enriques surfaces whose universal covers are singular K3 surfaces. If a singular K3 surface X has discriminant d, then it has a model over the ring class field d. Our main theorem is that the same holds true for any Enriques quotient of X. It is based on a study on Neron-Severi groups of singular K3 surfaces. We also comment on Galois actions on divisors of Enriques surfaces.
32 pages; v2: Section 2 expanded, minor additions and edits
- University of Hannover Germany
14J28, 11E16, 11G15, 11G35, 14J27, Mathematics - Number Theory, singular K3 surface, Néron–Severi group, Enriques surface, Mathematics - Algebraic Geometry, complex multiplication, 11E16, FOS: Mathematics, 11G35, 11G15, 14J27, Number Theory (math.NT), elliptic fibration, 14J28, Algebraic Geometry (math.AG), Mordell–Weil group
14J28, 11E16, 11G15, 11G35, 14J27, Mathematics - Number Theory, singular K3 surface, Néron–Severi group, Enriques surface, Mathematics - Algebraic Geometry, complex multiplication, 11E16, FOS: Mathematics, 11G35, 11G15, 14J27, Number Theory (math.NT), elliptic fibration, 14J28, Algebraic Geometry (math.AG), Mordell–Weil group
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